linprog — Solve linear programming minimization problems with inequality constraints, equality constraints, and bounds.

linprog minimizes f' * x subject to A*x <= b, Aeq*x == beq, and lb <= x <= ub. Supported forms are x = linprog(f,A,b), x = linprog(f,A,b,Aeq,beq), x = linprog(f,A,b,Aeq,beq,lb,ub), and the two-, three-, and four-output variants.

Syntax

x = linprog(f, A, b)
x = linprog(f, A, b, Aeq, beq)
x = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval] = linprog(f, A, b)
[x, fval] = linprog(f, A, b, Aeq, beq)
[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)

x = linprog(f, A, b)
x = linprog(f, A, b, Aeq, beq)
x = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval] = linprog(f, A, b)
[x, fval] = linprog(f, A, b, Aeq, beq)
[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval, exitflag] = linprog(f, A, b)
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq)
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq, lb, ub)
[x, fval, exitflag, output] = linprog(f, A, b)
[x, fval, exitflag, output] = linprog(f, A, b, Aeq, beq)
[x, fval, exitflag, output] = linprog(f, A, b, Aeq, beq, lb, ub)

Inputs

Returns

Returned values from linprog depend on how many outputs the caller requests.

Errors

How linprog works

• f, b, beq, lb, and ub must be numeric vectors with compatible lengths.
• A and Aeq must be numeric matrices with one column per element of f.
• [] may be passed for omitted optional Aeq, beq, lb, or ub arguments.
• exitflag is 1 when an optimum is found, -2 when no feasible point is found, and -3 when the objective is unbounded below.
• The fourth output is a struct with iterations, algorithm, constrviolation, and message fields.
• Advanced MATLAB options, algorithms, problem structs, and lambda outputs are intentionally unsupported in this initial implementation.

Examples

Solve a bounded linear program

f = [-1; -2];
A = [1 1];
b = 4;
[x, fval, exitflag] = linprog(f, A, b, [], [], [0; 0], [])

Expected output:

x =
     0
     4
fval =
    -8
exitflag =
     1

Use equality constraints and lower bounds

f = [1; 2];
A = [];
b = [];
Aeq = [1 1];
beq = 3;
[x, fval] = linprog(f, A, b, Aeq, beq, [1; 0], [])

Expected output:

x =
     3
     0
fval =
     3

Use a finite lower bound on one variable

f = [1; 0];
[x, fval, exitflag] = linprog(f, [], [], [], [], [2; -Inf], [])

Expected output:

x =
     2
     0
fval =
     2
exitflag =
     1

Optimize along an equality face

f = [-1; 0; 0];
A = [1 0 0];
b = 1;
Aeq = [0 0 1];
beq = 0;
[x, fval, exitflag] = linprog(f, A, b, Aeq, beq, [], [])

Expected output:

x =
     1
     0
     0
fval =
    -1
exitflag =
     1

Inspect infeasible status

[x, fval, exitflag, output] = linprog(1, [], [], [], [], 2, 1);
exitflag

Expected output:

exitflag =
    -2

Using linprog with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how linprog changes the result.

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how linprog is executed, line by line, in Rust.

• View the source for linprog in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

• RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
• Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing